Question

Find the number of sides of the regular polygon when the measure of an exterior angle is given.

Answer 1

$1.\\exterior\angle=30^\circ\\ exterior\angle=180^\circ-interior\ angle\\ interior\angle=180^\circ-exterior\ angle=180^\circ -30^\circ=150^\circ\\ \\Formula\ for\ number\ of\ sides\ of\ regular\ polygon:\\\\ interior\angle= 180^\circ-\frac{360^\circ}{n}\\ 150^\circ=180^\circ-\frac{360^\circ}{n}\\ -30^\circ=-\frac{360^\circ}{n}\ |*n\\ -30^\circ\ *n=-360^\circ \ |:-30^\circ\\ n=12\\\\ Number\ of\ sides\ is\ 12.$$2.\\exterior\angle=10^\circ\\ exterior\angle=180^\circ-interior\ angle\\ interior\angle=180^\circ-exterior\ angle=180^\circ -10^\circ=170^\circ\\ \\Formula\ for\ number\ of\ sides\ of\ regular\ polygon:\\\\ interior\angle= 180^\circ-\frac{360^\circ}{n}\\ 170^\circ=180^\circ-\frac{360^\circ}{n}\\ -10^\circ=-\frac{360^\circ}{n}\ |*n\\ -10^\circ\ *n=-360^\circ \ |:-10^\circ\\ n=36\\\\ Number\ of\ sides\ is\ 36.$